It is known that an .alpha.-olefin having 3 or more carbon atoms can be polymerized by using a catalyst composed of a solid catalytic ingredient in which a titanium tetrahalide is carried on a magnesium compound and another component which consists of an organic aluminium compound. With respect to the above-mentioned polymerization, various approaches have been attempted to provide a new method which is effective for increasing the yield of the resultant polymer per unit weight of the solid catalytic ingredient in the catalyst used, to such an extent that the resultant polymer contains a very small content of the used catalyst therein and, therefore, an operation for removing the used catalyst from the resultant polymer can be omitted.
However, the attempted approaches were unsatisfactory due to the following drawbacks.
1. The method failed to increase the yield of the polymer per unit weight of the solid catalytic component to such an extent that the removing operation for the used catalyst could be omitted.
2. The durability in the catalytic activity of the catalyst for the polymerization of the .alpha.-olefin is poor.
3. The sensitivity of the catalyst to hydrogen, which is used as a molecular weight-regulating agent for the polymer, is poor. Therefore, a large amount of hydrogen is necessary for regulating the molecular weight of the polymer.